U.S. patent number 6,256,099 [Application Number 09/426,319] was granted by the patent office on 2001-07-03 for methods and system for measuring three dimensional spatial coordinates and for external camera calibration necessary for that measurement.
Invention is credited to Jeffrey Brian Chow, Robert Newton James, Frederick Kaufman, Curtis Earle Lang.
United States Patent |
6,256,099 |
Kaufman , et al. |
July 3, 2001 |
**Please see images for:
( Certificate of Correction ) ** |
Methods and system for measuring three dimensional spatial
coordinates and for external camera calibration necessary for that
measurement
Abstract
The present invention relates to methods and system for
measuring three dimensional spatial coordinates and for external
camera calibration necessary for that measurement. A simple pattern
of light is projected onto a surface and used as a photogrammetric
target. Images of the simple pattern are captured by two or more
cameras, and processed by a computer provided with software using
conventional algorithms to identify homologous points. Either,
these points are used to calculate the external calibration of the
cameras, or they are used in conjunction with previously calculated
external camera calibration in order to calculate three dimensional
spatial coordinates on the surface of an object to be measured.
Inventors: |
Kaufman; Frederick (Vancouver,
B.C., CA), Chow; Jeffrey Brian (Vancouver, B.C.,
CA), James; Robert Newton (Burnaby, B.C.,
CA), Lang; Curtis Earle (late of North Vancouver,
CA) |
Family
ID: |
4163001 |
Appl.
No.: |
09/426,319 |
Filed: |
October 25, 1999 |
Foreign Application Priority Data
Current U.S.
Class: |
356/603 |
Current CPC
Class: |
G01B
11/2545 (20130101) |
Current International
Class: |
G01B
11/24 (20060101); G01B 11/25 (20060101); G01B
011/24 () |
Field of
Search: |
;356/376
;382/106,108,152-154,285,291,294,1 ;351/212,247,211 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Font; Frank G.
Assistant Examiner: Nguyen; Tu T.
Attorney, Agent or Firm: Kaufman; Frederick
Claims
The embodiments of the invention in which an exclusive property or
privilege is claimed are defined as follows:
1. Method of measuring three-dimensional spatial coordinates,
comprising the following operational steps:
A. synchronizing at least two cameras in order to capture
simultaneous images;
B. directing said cameras, kept in a fixed relationship, towards
the surface of an object to be measured;
C. projecting a simple pattern onto a portion of the surface of
said object, which portion is in the field of view of said
cameras;
D. capturing simultaneous images of said projected simple pattern
in said cameras;
E. using a computer, provided with software, using conventional
algorithms, for:
1. finding images of said projected simple pattern within said
captured images;
2. discarding said captured images and capturing new ones if images
of said pattern are not found within said captured images;
3. calculating centroids of said projected simple pattern on image
planes of said cameras;
4. grouping said calculated centroids into homologous pairs,
and
5. calculating three-dimensional coordinates from each of said
homologous pairs of centroids, internal and external camera
calibrations being known.
2. Method of measuring three-dimensional spatial coordinates, as
defined in claim 1, wherein the steps of discarding, calculating
and grouping are replaced, in the case where said projected simple
pattern is a spot, by the following:
A. discarding said captured images and capturing new ones if images
of the pattern are not found within both camera images, or if
multiple images of said spot are found within a single captured
image;
B. calculating two-dimensional centroids for the images of said
spot on the image planes of said cameras; and
C. grouping the resulting centroids as a homologous pair.
3. Method of measuring three-dimensional spatial coordinates, as
defined in claim 1, wherein the steps of calculating and grouping
are replaced, in the case where said projected simple pattern is a
stripe, by the following:
A. segmenting said images of said projected simple pattern, which
in this case is a stripe, into sets of one or more continuous
stripe images;
B. calculating, in one camera image, a plurality of one-dimensional
centroids across each continous stripe image at a known sampling
interval, which yields a series of two-dimensional points in said
camera image;
C. determining, for each two-dimensional point in said series, a
corresponding two-dimensional point on a stripe image in the other
camera image, internal and external camera calibrations being
known; and
D. grouping each such pair of corresponding two-dimensional points
as a homologous pair.
4. Method of external camera calibration, comprising the following
operational steps:
A. synchronizing at least two cameras in order to capture
simultaneous images;
B. directing said cameras towards a surface used for
calibration;
C. projecting a simple pattern onto a portion of said surface used
for calibration, which portion is in the field of view of said
cameras;
D. capturing a pair of simultaneous images of said projected simple
pattern;
E. using a computer, provided with software, using conventional
algorithms, for:
1. finding images of said projected simple pattern within said pair
of captured images;
2. discarding said captured images and capturing new ones if images
of said pattern are not found within said captured images;
3. calculating centroids of the projected pattern on the image
planes of said cameras;
4. grouping said calculated centroids into homologous pairs;
F. repeating steps C to E so as to obtain at least three homologous
pairs of centroids derived from projecting said simple pattern onto
different portions of said surface used for calibration;
G. using said computer, provided with software for photogrammetric
resection and ray bundle adjustment to compute an external
calibration, with relative scale, of the positions and orientations
of said cameras, and
H. transforming said relative scale to a usable absolute scale by
employing the system to measure a target of known dimensions, by
establishing the ratio between measured dimensions and known
dimensions, and by applying that ratio to the external
calibration.
5. System for carrying out a method for measuring three-dimensional
spatial coordinates, which method comprises the following
operational steps:
A. synchronizing at least two cameras in order to capture
simultaneous images;
B. directing said cameras, kept in a fixed relationship, towards
the surface of an object to be measured;
C. projecting a simple pattern onto a portion of the surface of
said object, which portion is in the field of view of said
cameras;
D. capturing simultaneous images of said projected simple pattern
in said cameras;
E. using software, employing conventional algorithms, for:
1. finding images of said projected simple pattern within said
captured images;
2. discarding said captured images and capturing new ones if images
of said pattern are not found within said captured images;
3. calculating centroids of said projected simple pattern on image
planes of said cameras;
4. grouping said calculated centroids into homologous pairs,
and
5. calculating three-dimensional coordinates from each of said
homologous pairs of centroids, internal and external camera
calibrations being known;
said system for carrying out said method for measuring
three-dimensional spatial coordinates including:
I. a light projector used to project a simple pattern onto a
surface;
II. at least two cameras containing image planes divided into a
multiplicity of photo-sensitive sites for capturing images; whereby
said cameras capture simultaneously exposed images of said
projected simple pattern, said images being transformed and stored
in a memory of the system;
III. data processing means, using conventional algorithms, for
carrying out said operational step E of said method for measuring
three-dimensional spatial coordinates.
6. System for carrying out a method for measuring three-dimensional
spatial coordinates, which method comprises the following
operational steps:
A. synchronizing at least two cameras in order to capture
simultaneous images;
B. directing said cameras, kept in a fixed relationship, towards
the surface of an object to be measured;
C. projecting a simple pattern in the form of a spot onto a portion
of the surface of said object, which portion is in the field of
view of said cameras;
D. capturing simultaneous images of said simple pattern in the form
of a spot in said cameras;
E. using software, employing conventional algorithms, for:
1. finding images of said simple pattern in the form of a spot
within said captured images;
2. discarding said captured images and capturing new ones, if
images of said simple pattern in the form of a spot are not found
within both camera images, or if multiple images of said simple
pattern in the form of a spot are found within a single captured
image;
3. calculating two-dimensional centroids for the images of said
simple pattern in the form of a spot on the image planes of said
cameras;
4. grouping the resulting centroids as a homologous pair; and
5. calculating three-dimensional coordinates from each of said
homologous pairs of centroids, internal and external camera
calibrations being known;
said system for carrying out said method for measuring
three-dimensional spatial coordinates including:
I. a light projector used to project a simple pattern in the form
of a spot onto a surface;
II. at least two cameras containing image planes divided into a
multiplicity of photo-sensitive sites for capturing images; whereby
said cameras capture simultaneously exposed images of said
projected simple pattern, said images being transformed and stored
in a memory of the system;
III. data processing means, using conventional algorithms, for
carrying out said operational step E of said method for measuring
three-dimensional spatial coordinates.
7. System for carrying out a method for measuring three-dimensional
spatial coordinates, which method comprises the following
operational steps:
A. synchronizing at least two cameras in order to capture
simultaneous images;
B. directing said cameras, kept in a fixed relationship, towards
the surface of an object to be measured;
C. projecting a simple pattern in the form of a stripe onto a
portion of the surface of said object, which portion is in the
field of view of said cameras;
D. capturing simultaneous images of said simple pattern in the form
of a stripe in said cameras;
E. using software, employing conventional algorithms, for:
1. finding images of said simple pattern in the form of a stripe
within said captured images;
2. discarding said captured images and capturing new ones, if
images of said simple pattern in the form of a stripe are not found
within both camera images, or if multiple images of said simple
pattern in the form of a stripe are found within a single captured
image;
3. segmenting said images of said projected simple pattern, which
in this case is a stripe, into sets of one or more continuous
stripe images;
4. calculating, in one camera image, a plurality of one-dimensional
centroids across each continous stripe image at a known sampling
interval, which yields a series of two-dimensional points in said
camera image;
5. determining, for each two-dimensional point in said series, a
corresponding two-dimensional point on a stripe image in the other
camera image, internal and external camera calibrations being
known;
6. grouping each such pair of corresponding two-dimensional points
as a homologous pair; and
7. calculating three-dimensional coordinates from each of said
homologous pairs of centroids, internal and external camera
calibrations being known;
said system for carrying out said method for measuring
three-dimensional spatial coordinates including:
I. a light projector used to project a simple pattern in the form
of a stripe onto a surface;
II. at least two cameras containing image planes divided into a
multiplicity of photo-sensitive sites for capturing images; whereby
said cameras capture simultaneously exposed images of said
projected simple pattern, said images being transformed and stored
in a memory of the system;
III. data processing means, using conventional algorithms, for
carrying out said operational step E of said method for measuring
three-dimensional spatial coordinates.
8. System for carrying out a method for external camera
calibration, which method comprises the following operational
steps:
A. synchronizing at least two cameras in order to capture
simultaneous images;
B. directing said cameras towards a surface used for
calibration;
C. projecting a simple pattern onto a portion of said surface used
for calibration, which portion is in the field of view of said
cameras;
D. capturing a pair of simultaneous images of said projected simple
pattern;
E. using software, employing conventional algorithms, for:
1. finding images of said projected simple pattern within said pair
of captured images;
2. discarding said captured images and capturing new ones if images
of said projected simple pattern are not found within said captured
images;
3. calculating centroids of said projected simple pattern on the
image planes of said cameras;
4. grouping said calculated centroids into homologous pairs;
F. repeating steps C to E so as to obtain at least three said
homologous pairs of centroids derived from projecting said simple
pattern onto different portions of said surface used for
calibration;
G. computing an external calibration, with relative scale, of the
positions and orientations of said cameras, using methods of
photogrammetric resection and ray bundle adjustment, and
H. transforming said relative scale to a usable absolute scale by
employing the system to measure a target of known dimensions, by
establishing the ratio between measured dimensions and known
dimensions, and by applying that ratio to the external
calibration.
said system including:
I. a light projector used to project a simple pattern onto a
surface used for calibration;
II. at least two cameras containing image planes divided into a
multiplicity of photo-sensitive sites for capturing images; whereby
said cameras capture simultaneously exposed images of said
projected simple pattern, said images being transformed and stored
in a memory of the system;
III. data processing means, using conventional algorithms, for
carrying out said operational steps E and G of said method for
external camera calibration.
Description
FIELD OF THE INVENTION
The present invention refers, in general, to methods and systems
for videogrammetry and, in particular, to methods and a system for
measuring three-dimensional spatial coordinates and for external
camera calibration required for that measurement.
BACKGROUND OF THE INVENTION
There is a known method in photogrammetry for analyzing
two-dimensional images, captured on photographic film, to produce
three-dimensional coordinate measurements. At least two images of
an overlapping surface portion are required. Modern photogrammetry
has incorporated computers to carry out many of its functions, but
the process has not yet been entirely automated. Videogrammetry has
added two major improvements to the art of photogrammetry. Firstly,
rather than recording images on film it records images directly on
opto-electronic imaging devices, such as photosensitive diodes or
other imaging surfaces. And secondly, since the images are
immediately digitized and stored in a computer, they are readily
accessible to manipulation and analysis by computational
methods.
Attempts have been made to develop better systems and methods for
measuring three-dimensional spatial coordinates. For example, U.S.
Pat. No. 5,589,942 dated Dec. 31, 1996, granted to Gordon, for a
"Real time three dimensional sensing system" discloses a system
which utilizes two flexibly located cameras for receiving and
recording visual information with respect to a sensed object
illuminated by a series of light planes. Each pixel of each image
is converted to a digital word and the words are grouped into
stripes, each stripe comprising contiguous pixels. One pixel of
each stripe in one image is selected and an epi-polar line of that
point is drawn in the other image. The three dimensional coordinate
of each selected point is determined by establishing the point on
said epi-polar line which also lies on a stripe in the second image
and which is closest to a known light plane. This system uses a
complex pattern of projected stripes, which creates difficulties in
finding homologous points in the pair of images, and leads to false
positives and false negatives in homologous point identification.
The system requires the light plane to be known.
U.S. Pat. No. 4,627,734, dated Dec. 9, 1986, granted to Rioux, for
a "Three dimensional imaging device and method" discloses a
three-dimensional imaging system operating in accordance with the
known active triangulation method, and employing a laser beam that
is projected onto an area of the surface to be examined. The
solution is characterized by synchronized scanning of projected and
deflected beams. The main disadvantage of the system consists in
the fact that the position and orientation of the projected light
beam must be known in order to calculate three dimensional
coordinates.
U.S. Pat. No. 5,440,392 dated Aug. 8, 1995, granted to Pettersen et
al. for a "Method and system for point by point measurement of
spatial coordinates" describes a technical solution for point by
point measurement of spatial coordinates. A touch probe, including
three point-sized light sources at known local coordinates, touches
the point to be measured. Using a camera to acquire an image of the
three light sources, the system calculates the three dimensional
coordinates of the point touched. It is obvious that this solution
requires physically touching the object to be measured and is
time-consuming.
SUMMARY OF THE INVENTION
There is accordingly a need for a method and system which overcome,
or at least alleviate, the disadvantages of the prior art. It is
therefore desirable to offer a technical solution which is faster,
non-contact, and calibrated quickly and easily, without the use of
special equipment.
Broadly, the method of measuring three-dimensional spatial
coordinates starts by synchronizing at least two cameras so that
they can capture simultaneous images. Then the cameras are set up
with the object to be measured in their fields of view. A simple
pattern is then projected onto the surface of the object, and
simultaneous images which include the projected pattern are
captured. The images are processed by a computer, which uses
conventional software algorithms to find the pattern images,
calculate centroids from the pattern images, group the centroids
into homologous pairs, and calculate three-dimensional spatial
coordinates.
In one aspect of the above method, wherein the projected simple
pattern is a spot, images are discarded and recaptured, if
necessary, until there is just one centroid in each camera image.
Therefore, grouping these centroids into a homologous pair is
trivial.
In another aspect of the above method, wherein the projected simple
pattern is a stripe, it is necessary to segment the stripe images
into sets of continuous stripe images. In one camera image, each
continous stripe image is sampled at a known interval, and a
centroid is calculated across the stripe for each sample, yielding
a series of two dimensional points in the camera image. For each
point in the series, the known internal and external calibrations
of both cameras are used to determine a corresponding
two-dimensional point on a stripe within the other camera image.
Each such pair of corresponding points are grouped as a homologous
pair.
Generally, the method of external camera calibration starts by
synchronizing at least two cameras, so that they capture
simultaneous images. Then, the cameras are placed so that their
fields of view include a surface that will be used for calibration,
and a simple pattern is projected onto that surface. A pair of
simultaneous images of the simple pattern are captured. The images
are processed by a computer, which uses conventional software
algorithms to find the pattern images, to discard any images in
which the pattern is not found, to calculate centroids of the
pattern images, and to group the centroids into homologous pairs.
Then, the pattern is projected onto a different portion of the
surface, and new images are captured and processed, until the
required number of homologous pairs have been found. The computer
uses software for the methods of resection and ray bundle
adjustment, known in photogrammetry, to compute an external
calibration, with relative scale, of the positions and orientations
of the cameras. Then, the system is used to acquire
three-dimensional spatial coordinates from the surface of a target
object of known dimensions. From this, a ratio is calculated and
applied to the external calibration, in order to transform the
relative scale into a usable absolute scale.
Broadly, the system used to carry out the above methods comprises a
computer provided with software to execute the methods, at least
two cameras containing image planes divided into a multiplicity of
photosensitive sites, and a light projector capable of projecting a
simple pattern onto a surface. Simultaneously exposed images of the
simple pattern are captured and stored in computer memory.
Alternatively, the system can use charge couple devices, charge
injection devices, or complementary metal-oxide semiconductors for
image planes.
Alternatively, the system can use a light projector that is
hand-held or coupled to a computer-controlled electro-mechanical
beam positioner.
Alternatively, the system can use a light projector that is a laser
device, a light-emitting diode (LED) device, or a light projector
using focussing optics to project an image onto an external
surface.
Alternatively, the system can use a light projector that uses
collimating or focussing optics.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 depicts the system for carrying out the present invention,
and
FIG. 2 depicts the use of a projected stripe for external camera
calibration.
DESCRIPTION OF PREFERRED EMBODIMENTS
Referring now to the accompanying FIG. 1, there is depicted a
system for measuring three-dimensional spatial coordinates and for
external camera calibration 10, which comprises a computer 12 with
image capture electronics boards 14 to which are connected two
cameras 16 and 18. Alternatively, more cameras may be added, if
required, for more complete coverage of the surface. A light
projector 20 is used to project a simple pattern 22, such as a
small spot of which the image approximates a point light source,
onto a surface 24. Alternatively, simple pattern 22 may be a larger
spot, of which the image is a disk, or it may be a stripe.
Simultaneously-exposed images of projected simple pattern 22 are
produced by cameras 16 and 18, then captured by image capture
electronics boards 14, and finally stored in the memory of computer
12. Computer 12 is provided with software to control cameras 16 and
18 and to process and analyze the images. Cameras 16 and 18 contain
imaging surfaces, which are charge-couple devices (CCD). The
imaging surfaces are divided into a multiplicity of photo-sensitive
sites.
Alternatively, cameras 16 and 18 may contain imaging surfaces which
are charge injection devices (CID) or complementary metal-oxide
semiconductor (CMOS) devices.
Light projector 20 is hand-held. Alternatively, light projector 20
is coupled to a computer-controlled electro-mechanical beam
positioner capable of altitude/azimuth movement.
Light projector 20 is a laser device. Alternatively, light
projector 20 is a light-emitting diode (LED) device or a slide
projector.
Light projector 20 uses a coherent light source. Alternatively,
light projector 20 can use an incoherent light source.
Light projector 20 uses collimating optics. Alternatively, light
projector 20 can use focussing optics.
In the case of a laser or LED device, beam forming optics that
expand the light in the shape of a flat fan can be used.
In the case of a slide projector, the slide comprises an opaque
mask surrounding a transparent pattern which is one of the
above-mentioned three simple patterns: a small spot, a larger spot,
or a stripe.
The components of the system mentioned in the above description are
of conventional type and are readily available.
The system described above is used to measure three-dimensional
spatial coordinates as follows: Cameras 16 and 18 are synchronized
in order to capture simultaneous images. Then, cameras 16 and 18,
kept in a fixed relationship, are directed towards the surface of
an object to be measured. Then, a simple pattern is projected onto
a portion of the surface of the object, which portion is in the
field of view of both cameras 16 and 18. Image capture electronics
boards 14 are used to capture simultaneous images of the projected
simple pattern in cameras 16 and 18. Computer 12 is provided with
software, using conventional algorithms, to perform the following
operations:
images of the projected pattern are found within the captured
images;
if images of the pattern are not found within both camera images,
the camera images are discarded, the pattern is moved, and new
images are captured;
centroids of the projected pattern on the image planes of cameras
16 and 18 are calculated;
the above-calculated centroids are grouped into homologous pairs (a
pair of centroids is homologous if they are centroids of two images
of the same portion of the same simple pattern), and
three-dimensional coordinates are calculated from each homologous
pair of centroids, internal and external camera calibrations being
known.
Some of the above operations differ depending on the type of
projected simple pattern.
If the projected simple pattern is a spot, the above operations,
except the first and the last, are replaced by the following:
the camera images are discarded and new ones captured, if images of
the pattern are not found within both camera images, or if multiple
images of the pattern are found within a single camera image;
two-dimensional centroids are calculated, for the images of the
spot, on the image planes of cameras 16 and 18, and
the resulting centroids are grouped as a homologous pair.
If the projected simple pattern is a stripe, the above operations,
except the first and the last, are replaced by the following:
the stripe image within each camera image is segmented into a set
of one or more continuous stripe images;
in one camera image, one-dimensional centroids are calculated
across each continous stripe image at a known sampling interval,
which yields a series of two-dimensional points on the image
plane;
for each two-dimensional point in the series, a corresponding
two-dimensional point on a stripe image in the other camera image
is found, using the known internal and external camera
calibrations, and
each such pair of corresponding two-dimensional points is grouped
as a homologous pair.
An external camera calibration determines the positions and
orientations of the cameras. The external camera calibration, along
with the already-established internal camera calibration and the
homologous pairs, mentioned above, is necessary for using the
system to calculate three-dimensional spatial coordinates, as
described above. To perform external camera calibration, the
system, in the case where the simple pattern is a spot, is used as
follows:
1. Cameras 16 and 18 are synchronized in order to capture
simultaneous images and are directed independently towards a
surface used for calibration.
2. A simple spot pattern is projected onto a portion of the said
surface used for calibration, which portion is located in the field
of view of both cameras 16 and 18.
3. A pair of images of the projected simple pattern is captured
simultaneously.
4. Computer 12 is provided with software, using conventional
algorithms, to perform the following operations:
images of the projected pattern within the captured images are
found; if no images of the pattern are found, or multiple images of
the pattern are found within a camera image, the camera images are
discarded, the projected pattern is moved, and new camera images
are captured;
centroids of the projected pattern, on the image planes of cameras
16 and 18, are calculated;
the above-calculated centroids are grouped into homologous
pairs;
5. Operations 2 to 4 are repeated, so as to obtain at least three
homologous pairs of centroids derived from projecting the simple
pattern onto different portions of the surface used for
calibration.
6. Computer 12, provided with software, applies the methods of
resection and ray bundle adjustment, known in photogrammetry, to
calculate a partial external calibration, with an unknown absolute
scale, of the positions and orientations of cameras 16 and 18.
7. An absolute scale is determined by using the system to measure a
target of known dimensions, then establishing the ratio between
measured dimensions and known dimensions, and applying that ratio
to the already-calculated partial external calibration.
In the case where the simple pattern is a stripe, the system is
used as follows (FIG. 2):
1. Cameras 16 and 18 are synchronized in order to capture
simultaneous images and are directed independently towards a
surface used for calibration 24'.
2. Surface used for calibration 24' comprises planes that intersect
so that their lines of intersection are in the fields of view of
cameras 16 and 18.
3. A simple pattern 22', which in this case is a stripe, is
projected onto a portion of surface used for calibration 24', which
portion is located in the field of view of both cameras 16 and 18,
so that the stripe crosses the said lines of intersection.
4. A pair of camera images 26 containing projected simple pattern
22' is captured simultaneously.
5. Computer 12 is provided with software, using conventional
algorithms, to perform the following operations:
a pair of stripe images 28 of projected simple pattern 22', within
pair of camera images 26, already captured, are found; if no images
of projected simple pattern 22' are found, or multiple images of
projected simple pattern 22' are found within either one of pair of
camera images 26, that pair of camera images 26 is discarded, then
projected simple pattern 22' is moved, and a new pair of camera
images 26 is captured;
in camera images 26, one-dimensional centroids are calculated
across each image of the pair of stripe images 28, at a known
sampling interval, which yields a series of two-dimensional points
on the image plane;
each stripe image of the pair of stripe images 28 is divided into
straight-line segments;
the intersection points of adjoining straight-line segments are
found in both of the pair of stripe images 28;
the found intersection points are grouped into homologous pairs, in
order, from top to bottom of each image;
6. If the necessary minimum number of homologous pairs of
intersection points is not obtained, projected simple pattern 22'
is moved to a new position on surface used for calibration 24' and
operations 3 to 5 are repeated.
7. Computer 12, provided with software, applies the methods of
resection and ray bundle adjustment, known in photogrammetry, to
calculate a partial external calibration, with an unknown absolute
scale, of the positions and orientations of cameras 16 and 18.
8. An absolute scale is determined by using the system to measure a
target of known dimensions, then establishing the ratio between
measured dimensions and known dimensions, and applying that ratio
to the already-calculated partial external calibration.
At this stage the external calibration is complete, and the system
can be used to measure three-dimensional spatial coordinates.
The system and its uses, described above, are based on the same
inventive concept, which consists in projecting a simple pattern to
generate homologous points for use with standard photogrammetric
techniques.
* * * * *